Question

What is the slope-intercept form of the equation of the line that passes through the points (−3, 2) and (1, 5) ?

y=3/4x+72

y=3/4x−92

y=3/4x+17/4

y=3/4x−74

The answer is C: y= 3/4x+17/4

Answer 1

C

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)

m =
`(5-2)/(1+3)` =
`(3)/(4)`, thus

y =
`(3)/(4)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 3, 2), then

2 = -
`(9)/(4)` + c ⇒ c =
`(17)/(4)`

y =
`(3)/(4)` x +
`(17)/(4)` → C